This can either mean predicting a) that certain theories will be accepted as well tested, or b) that we will derive new explanations or predictions from other theories.
If we predict what theories others will accept, a), the forecast clearly needs to be kept secret from the people in question lest it influence them now (as Popper calls it, the 'Oedipus-effect'). If we keep the prediction secret, either it becomes a prediction from without—and therefore is not self-prediction—or it still requires us to predict that we will keep our results secret. Yet whether we decide to keep our results secret will depend on future circumstances, which in turn depend on the growth of our own knowledge—so to assume we can predict our own adherence to secrecy begs the question of whether self-prediction is possible.
Popper argues that we similarly cannot predict the future acceptance of a new theory in the light of new evidence or argument. If that information is available now, the new theory is also available now. If we're talking about evidence that is not presently available, that we can predict its existence using our current theories makes any new theory superfluous.